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Constructing a Generator of Matrices with Pattern

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  • Halkos, George
  • Tsilika, Kyriaki

Abstract

Computations with large matrices work out faster with computer software, even faster creating automatically the matrix of the size and pattern needed. In this paper we propose free computer algebra system Xcas resources to display particular matrices that can be called up directly. Our computer codes provide shortcuts for entering random block diagonal matrices, random triangular matrices, random and specialized band matrices, elementary matrices Eij, Fourier matrices. As for matrices needed in the study of mathematical issues concerning the properties of the roots of a polynomial, we create features with polynomial coefficients. We also propose codes for immediate construction of functional matrices such as Jacobian, bordered Hessian and Wronskian. The computer codes proposed provide visual representation of the matrix pattern (which is traditionally explained using indices and numerals), infinite number of examples using random numbers and immediate construction of large matrices of various forms.

Suggested Citation

  • Halkos, George & Tsilika, Kyriaki, 2012. "Constructing a Generator of Matrices with Pattern," MPRA Paper 43614, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:43614
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    References listed on IDEAS

    as
    1. Lloyd, William P & Lee, Cheng F, 1976. "Block Recursive Systems in Asset Pricing Models," Journal of Finance, American Finance Association, vol. 31(4), pages 1101-1113, September.
    2. George Halkos & Kyriaki Tsilika, 2015. "Programming Identification Criteria in Simultaneous Equation Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 157-170, June.
    3. David G. Tarr, 2017. "Distributed Lags, Morishima Matrices, And The Stability Of Economic Models," World Scientific Book Chapters, in: Trade Policies for Development and Transition, chapter 27, pages 627-630, World Scientific Publishing Co. Pte. Ltd..
    4. Arthur F. Veinott, 1969. "Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems," Operations Research, INFORMS, vol. 17(2), pages 262-291, April.
    5. Halkos, George & Tsilika, Kyriaki, 2012. "Stability analysis in economic dynamics: A computational approach," MPRA Paper 41371, University Library of Munich, Germany.
    6. Geoffrey J.D. Hewings, 1985. "Regional Input-Output Analysis," Wholbk, Regional Research Institute, West Virginia University, number 11 edited by Grant I. Thrall, Fall.
    7. Batten, D & Martellato, D, 1985. "Classical versus Modern Approaches to Interregional Input-Output Analysis," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 19(3), pages 1-15, November.
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    More about this item

    Keywords

    Matrices with pattern; functional programming; computer software;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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